9,055 reputation
51106
bio website linkedin.com/in/nikov
location Redmond, WA
age 35
visits member for 2 years, 8 months
seen 8 hours ago

Having more than 12 years of experience in software development and testing, I currently work at Microsoft on the next generation of managed compilers, programming language tools and IDE. Among other things, my job involves participation in design of type systems and language features, checking them for soundness, their actual implementation and testing.

Although I am not a professional mathematician, I hold a degree in theoretical physics, and I am very passionate about mathematics, especially about evaluation of integrals, sums and products in a closed form, foundations of mathematics, order theory, type theory, computability theory, graph theory and combinatorics.

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Feel free to contact me at <ɯoɔ·ןᴉɐɯᵷ(ʇɐ)ʌoʞᴉuʇǝɥsǝɹ·ʌ>


10h
asked Packing an infinite sequence of disks
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
29
awarded  Favorite Question
Jun
28
awarded  Necromancer
Jun
20
awarded  Favorite Question
Jun
18
accepted Integrals of $\sqrt{x+\sqrt{\phantom|\dots+\sqrt{x+1}}}$ in elementary functions
Jun
18
awarded  Popular Question
Jun
17
comment Covering $\mathbb R^2$ with function graphs
IIRC, Baire category theorem gives us that $\mathbb R^2$ is not a countable union of closed sets with empty interior. A function graph is not necessary a closed set, e.g. the graph of Dirichlet function.
Jun
17
comment Covering $\mathbb R^2$ with function graphs
@user99680 Each graph can have a unique shape and is not necessary a line — a function can be discontinuous at every point, and its graph can even be dense in $\mathbb R^2$
Jun
17
comment Covering $\mathbb R^2$ with function graphs
@user99680 To generate an uncountable set is not a problem — each graph itself is an uncountable set of points. The interesting question is to how to cover the whole plane (if it is possible at all)?
Jun
17
comment Covering $\mathbb R^2$ with function graphs
@user99680 That would be an uncountable family of lines, but the question says the total number of graphs must be countable.
Jun
15
comment How did Kurt Gödel's Incompleteness Theorem affect the mathematical world?
I would highly recommend to read the book "Inexhaustibility: a non-exhaustive treatment" by Torkel Franzén.
Jun
15
revised Relations between definite integrals not having a known closed form
added 33 characters in body
Jun
14
comment Consistency of Peano axioms (Hilbert's second problem)?
Let's fix an inconsistent statement such as $0=1$. In fact, for every natural number $n$, $\sf PA$ can prove that there is no formal proof of length $\le n$ in $\sf PA$ of $0=1$. But $\sf PA$ cannot prove the natural final step — a single universally quantified statement "$\forall n$, there is no formal proof of length $\le n$ in $\sf PA$ of $\ 0=1$". Some people infer this final step informally, not realizing that it cannot be done formally in $\sf PA$.
Jun
14
revised Relations between definite integrals not having a known closed form
tags
Jun
14
awarded  Good Question
Jun
14
asked Relations between definite integrals not having a known closed form
Jun
13
revised Integrals of $\sqrt{x+\sqrt{\phantom|\dots+\sqrt{x+1}}}$ in elementary functions
added 205 characters in body; edited tags
Jun
8
accepted Meaning of the Axiom of regularity (foundation)